The Knesset House Committee is expected to convene Monday to approve the split.
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Sheetrit spoke to Kadima Chairman Shaul Mofaz on Sunday and informed him of his decision to leave the party in favor of Livni's party.
Six Knesset members have already agreed to split from Kadima: Rachel Adatto, Majalli Whbee, Orit Zuaretz, Robert Tibayev, Shlomo Molla and Yoel Hasson.
Livni was in need of seven MKs in order to receive campaign funding rights.
Former State Comptroller Micha Lindenstrauss decided over the weekend to reject Livni's offer to join her party. Former Labor Chairman Amram Mitzna, on the other hand, accepted a similar offer.
Another party newcomer is Merav Cohen, a social activist and Jerusalem city council member. Cohen, founded the Hitorerut ("awakening") movement, which attempted to keep a young and working population in Jerusalem, waged city wide social campaigns and headed a local entrepreneurship with the attempt to foster the economy and community life.
Moran Azulay contributed to this report
Yuval Karni and Moran Azulay are Ynet and Yedioth Ahronoth correspondents
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